Algorithms for Triangulated Terrains

Digital elevation models can represent many types of geographic data. One of the common digital elevation models is the triangulated irregular network (also called TIN, or polyhedral terrain, or triangulated terrain). We discuss ways to represent a TIN in a data structure, and give some of the basic algorithms that work on TINs. These include retrieving contour lines, computing perspective views, and constructing TINS from other digital elevation data. We also give a recent method to compress and decompress a TIN for storage and transmission purposes.

[1]  E. Lynn Usery,et al.  Geographical Information Systems: Principles and Applications , 1992 .

[2]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[3]  Kenneth L. Clarkson,et al.  Applications of random sampling in computational geometry, II , 1988, SCG '88.

[4]  David J. Maguire,et al.  Geographical information systems : principles and applications , 1991 .

[5]  M. Garland,et al.  Fast Polygonal Approximation of Terrains and Height Fields , 1998 .

[6]  Marc J. van Kreveld,et al.  Efficient Methods for Isoline Extraction from a TIN , 1996, Int. J. Geogr. Inf. Sci..

[7]  Marc J. van Kreveld,et al.  Digital Elevation Models and TIN Algorithms , 1996, Algorithmic Foundations of Geographic Information Systems.

[8]  J. Casalí,et al.  Digital Terrain Modelling of Drainage Channel Erosion , 1999 .

[9]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[10]  S S Stevens,et al.  On the Theory of Scales of Measurement. , 1946, Science.

[11]  Mark de Berg,et al.  Visualization of TINs , 1996, Algorithmic Foundations of Geographic Information Systems.

[12]  Joseph O'Rourke,et al.  Computational Geometry in C. , 1995 .

[13]  David P. Dobkin.  Computational geometry and computer graphics , 1992 .

[14]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[15]  Marc J. van Kreveld,et al.  Good orders for incremental (re)construction , 1997, SCG '97.

[16]  Leila De Floriani,et al.  Extracting contour lines from a hierarchical surface model , 1993, Comput. Graph. Forum.

[17]  Andrzej Lingas,et al.  On computing Voronoi diagrams for sorted point sets , 1995, Int. J. Comput. Geom. Appl..

[18]  W. Randolph Franklin.  Compressing Elevation Data , 1995, SSD.

[19]  David G. Kirkpatrick,et al.  Optimal Search in Planar Subdivisions , 1983, SIAM J. Comput..

[20]  Marc J. van Kreveld,et al.  Linear-Time Reconstruction of Delaunay Triangulations with Applications , 1997, ESA.

[21]  Norma Banas,et al.  Visualization , 1968, Machine-mediated learning.

[22]  Robin Thomas,et al.  Efficiently four-coloring planar graphs , 1996, STOC '96.

[23]  R. Seidel.  Backwards Analysis of Randomized Geometric Algorithms , 1993 .

[24]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[25]  Alan M. MacEachren,et al.  Visualization in modern cartography , 1994 .

[26]  Norishige Chiba,et al.  A Linear 5-Coloring Algorithm of Planar Graphs , 1981, J. Algorithms.

[27]  Wm. Randolph Franklin.  Lossy Compression of Elevation Data , 1996 .